Marriage and Roommate

IF 0.6 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
Kazuo Iwama, Shuichi Miyazaki
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引用次数: 0

Abstract

This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance [Formula: see text] is a stable matching (that however must satisfy a certain condition) of some marriage instance [Formula: see text]. [Formula: see text] is obtained just by making two copies of [Formula: see text], one for the men’s table and the other for the women’s table. The second objective is to investigate the possibility of reducing the roommate problem to the marriage problem (with one-to-one correspondence between their stable matchings) in polynomial time. For a given [Formula: see text], we construct the rotation POSET [Formula: see text] of [Formula: see text] and then we “halve” it to obtain [Formula: see text], by which we can forget the above condition and can use all the closed subsets of [Formula: see text] for all the stable matchings of [Formula: see text]. Unfortunately this approach works (runs in polynomial time) only for restricted instances.
婚姻与室友
本文有两个目的。一是给出一个线性时间算法,利用稳定婚姻问题求解稳定室友问题(即得到一个稳定匹配)。其思想是,室友实例的稳定匹配[公式:见文本]是某些婚姻实例的稳定匹配(但必须满足特定条件)[公式:见文本]。只需将[公式:见文]复制两份即可得到[公式:见文],一份用于男子牌桌,另一份用于女子牌桌。第二个目标是研究在多项式时间内将室友问题简化为婚姻问题的可能性(他们的稳定匹配之间有一对一的对应关系)。对于给定的[Formula: see text],我们构造[Formula: see text]的旋转POSET [Formula: see text],然后将其“对半”得到[Formula: see text],这样我们就可以忽略上述条件,并且可以使用[Formula: see text]的所有闭子集来进行[Formula: see text]的所有稳定匹配。不幸的是,这种方法只适用于有限的实例(在多项式时间内运行)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Foundations of Computer Science
International Journal of Foundations of Computer Science 工程技术-计算机:理论方法
CiteScore
1.60
自引率
12.50%
发文量
63
审稿时长
3 months
期刊介绍: The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing
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